Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets
Classical Analysis and ODEs
2021-02-23 v3 Analysis of PDEs
Abstract
A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and vanishing trace on a part of the boundary of an open set is established. Geometric assumptions are of mostly measure theoretic nature and reach beyond Lipschitz regular domains. Previous results were limited to regular geometric configurations or Hilbertian Sobolev spaces. Sets with porous boundary and their characteristic multipliers on smoothness spaces play a major role in the arguments.
Cite
@article{arxiv.1807.02293,
title = {Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets},
author = {Sebastian Bechtel and Moritz Egert},
journal= {arXiv preprint arXiv:1807.02293},
year = {2021}
}
Comments
Upload of the published version including the correction of some further typos